Question

Peter invests $100,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?

Answer 1

$682.50

Step-by-step explanation:

Given;

The amount invested by the Peter = $100,000

Interest rate = 12% annually

The amount invested by the Martha = $100,000

Interest rate = 12% compounded monthly

Now,

The Total amount received by the Peter at the end of the year

= Amount invested × ( 1 + Annual interest rate )

= $100,000 × ( 1 + 0.12 )

= $112,000

The amount received by the Martha

since it is compounded monthly,

we have

Amount received by Martha = Amount invested × ( 1 + r )ⁿ

here,

r is the monthly return i.e 12% / 12 = 1%

n is the time period in months = 1 year = 12 months

thus, on substituting the respective values, we get

Amount received Martha = $100,000 × ( 1 + 0.01 )¹²

or

The amount received by Martha = $112,682.50

Hence,

The amount of more money Martha have = $112,682.50 - $112,000

or

The amount of more money Martha have = $682.50